Skew Fibonacci Algebras: Non-Commutative Extensions via Ore Extensions

I introduce a family of non-commutative algebras called Skew Fibonacci Algebras, constructed as iterated Ore extensions of R by generators ω₁, ..., ωₘ satisfying ωᵢ² = ωᵢ + 1 and ωⱼ ωᵢ = σ(ωᵢ) ωⱼ for i < j, where σ is an automorphism of the Fibonacci relation. I prove that these algebras are associative by construction, establish the Fibonacci structure ωᵢⁿ = Fₙωᵢ + Fₙ₋₁, and classify the automorphisms that preserve the defining relation. I construct explicit examples using σ(ω) = ω (commutative case) and σ(ω) = ω⁻¹ = ω - 1 (non-commutative case). I also determine the center and a canonical vector space basis of dimension 2ᵐ. This work provides a rigorous framework for non-commutative Fibonacci algebras with potential applications to quantum groups and mathematical physics.